K-Distribution and Polarimetric Terrain Radar Clutter

Abstract A multivariate K- distribution is proposed to model the statistics of fully polarimetric radar data from earth terrain with polarizations HH, HV, VH, and VV. In this approach, correlated polarizations of radar signals, as characterized by a covariance matrix, are treated as the sum of N n- dimensional random vectors; N obeys the negative binomial distribution with a parameter α and mean N. Subsequently, an n- dimensional K- distribution, with either zero or nonzero mean, is developed in the limit of infinite N or illuminated area. The probability density function (PDF) of the K- distributed vector normalized by its Euclidean norm is independent of the parameter α and is the same as that derived from a zero-mean Gaussian-distributed random vector. The above model is well supported by experimental data provided by MIT Lincoln Laboratory and the Jet Propulsion Laboratory in the form of polarimetric measurements.